Armed officers were sent to the scene of a “serious incident” where a police firearm was discharged and a man was shot.
Police said firearms officers attended the scene and the man was located.
A police firearm was discharged and the man sustained a gunshot injury, the Met said.
Police said there does not appear to be an ongoing threat to the wider public and no other injuries have been reported.
Gemma Daly, 31, from Whitstable, but staying in Greenwich, said she heard some shouting and then “a big bang” which she believes was a gunshot.
She said she heard police sirens straight away, adding that the emergency services then started arriving.
“Police were attending to a man on the side of the bridge,” she said, adding that he was “clearly injured”.
“They removed his clothing”, she said, describing how “a lot of people” were working on the man before he was put on a stretcher.
Ms Daly said police “started to go around” a silver car, which was still on the bridge.
Pictures of the scene showed emergency vehicles, including police cars and an ambulance, stopped in the middle of the road.
Greenwich MPS tweeted: “We are responding to a serious incident in #Greenwich.
“Armed officers are on the scene.
“We will provide further updates when we can.”
A London Ambulance Service spokesperson said: “We sent a number of resources including an ambulance crew, an advanced paramedic, a motorcycle paramedic, a medic in a fast response car and an incident response officer, and we also dispatched medics from London’s Air Ambulance.
“We treated a man at the scene and took him as a priority to a major trauma centre.”
A spokesperson for London’s Air Ambulance said: “Our advanced trauma team was dispatched via aircraft by London Ambulance Service at 1447 today to reports of a shooting in the Greenwich area.
“After treatment on scene the patient was transferred by road to a major trauma hospital accompanied by London’s Air Ambulance.”
Police said the Directorate of Professional Standards has been informed.